On the effect of damping on dispersion curves in plates

1 Computer Aided Engineering Design and Product Development, The Faculty of Engineering and Science, Aalborg University, VBN2 Department of Mechanical and Manufacturing Engineering, The Faculty of Engineering and Science, Aalborg University, VBN3 Solid and Computational Mechanics, The Faculty of Engineering and Science, Aalborg University, VBN4 The Faculty of Engineering and Science, Aalborg University, VBN5 Department of Industrial Engineering, University of Parma, Italy

DOI:

10.1016/j.ijsolstr.2013.02.016

Abstract:

This paper presents a study on quantitative prediction and understanding of time-harmonic wave characteristics in damped plates. Material dissipation is modelled by using complex-valued velocities of free dilatation and shear waves in an unbounded volume. As a numerical example, solution of the classical Rayleigh–Lamb problem for a viscoelastic plate is presented to illustrate and discuss the role of dissipation in the cut-off phenomenon and in the phenomenon of veering for dispersion curves. These phenomena are explained in more detail considering a simple model, which allows accurate asymptotic analysis of the perturbation of dispersion curves in the regions of cut-off and veering.